Numerical Methods for Civil Engineers Numerical Methods for Civil Engineers Welcome to ภาคการศึกษาที่ 3 ปการศึกษา 2548 Instructor: Mongkol JIRAVACHARADET Instructor: Mongkol JIRAVACHARADET School of Civil Engineering Institute of Engineering Suranaree University of Technology Lecture 1 - MATLAB Introduction Textbook Textbook Applied Numerical Methods Applied Numerical Methods With MATLAB for Engineers With MATLAB for Engineers and Scientists and Scientists STEVEN C. CHAPRA STEVEN C. CHAPRA McGraw-Hill International Edition
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Numerical Methods for Civil EngineersNumerical Methods for Civil Engineers
Development Environment: set of tools and facilities that help you use MATLAB functions and files. Many of these tools are graphical user interfaces. It includes the MATLAB desktop and Command Window, a command history, an editor and dedugger, and browsers for viewing help, the workspace, files, and the search path.
The MALAB Mathematical Function Library: a vast collection of computational algorithms.
The MATLAB Language: This is a high-level matrix/array language with control flow statements, functions, data structures, input/output, and objected-oriented programming features.
Graphics: MATLAB has extensive facilities 2-D and 3-D data visualization, animation, and presentation graphics.
The MATLAB Application Program Interface (API): allows you to write C and Fortran programs that interact with MATLAB.
Getting Started
MATLAB Desktop
Getting Started
Command Window
Command prompt >> DEMO
Getting Started
Editor/Debugger
Basic Arithmetic
Last-line editing
Calculator functions work as you'd expect:
>>(1+4)*3
ans =
15+ and - are addition, / is division, * is multiplication, ^ is an exponent.
>> 5*5*5>> 5^(-2.5)>> 3*(23+14.7-4/6)/3.5
Up Arrow
>> 2 + 6 - 4ans =
4
The value in ans can be recalled:
>> ans/2
ans = 2
Assign value to a variable:
>> a = 5
>> b = 6
>> c = b/a
>> a=2;>> A=3;>> 2*a>> 2*A
Upper & Lower Case
Several commands in the same line:>>x=2;y=6+x,x=y+7
… For too long command:>> Num_Apples = 10;>> Num_Orange = 25;>> Num_Pears = 12;>> Num_Fruit=Num_Apples+Num_Orange...+ Num_Pears
sin(x), cos(x), tan(x),
sqrt(x), log(x), log10(x),
asin(x), acos(x), atan(x)
Built-in Functions
>> sin(pi/4)ans =
0.7071
>> pians =
3.1416
The output of each command can be suppress by using semicolon ;
>> x = 5;>> y = sqrt(59);>> z = log(y) + x^0.25z =
3.5341
The commas allow more than one commandon a line:
>> a = 5; b = sin(a), c = sinh(a)b =-0.9589
c = 74.2099
MATLAB Variables is created whenever it appearson the left-hand of “ = “
>> t = 5;>> t = t + 2t =
7
Format
>> pi>> format long>> pi>> format short>> format bank>> format short e>> format long e>> format compact>> format loose>> format
Any variable appearing on the right-hand side of“ = “ must already be defined.
>> x = 2*z??? Undefined function or variable ‘z’
Use long variable names is better to rememberand understandable for others
>> radius = 5.2;>> area = pi*radius^2;
>> who>> whos>> clear
Built-in VariablesUse by MATLAB, Should not be assigned to other values
Variable Meaning
ans value of an expression when not assigned to variable
eps floating-point precision
i, j unit imaginary numbers, i = j =pi π = 3.14159265 . . .
realmax largest positive floating-point number
realmin smallest positive floating-point number
Inf ∞, a number larger than realmax, result of 1/0
NaN not a number (0/0)
1−
>> x = 0;>> 5/x>> x/x
>> help log
>> lookfor cosineOn-line Help:
Matrices and Magic SquaresMatrices and Magic Squares
MATLAB allows you to work with entire matrices quickly and easily.
In MATLAB, a matrix is a rectangular array of numbers.
scalars = 1-by-1 matrices
vectors = one row or column matrices
Renaissance engraving Melencolia I by the German artist and amateurmathematician Albrecht Dürer.
The matrices operations in MATLAB are designed to be as natural as possible.
it is usually best to think of everything as a matrix.
Entering MatricesEntering Matrices
Start by entering matrix as a list of its elements.
You only have to follow a few basic conventions:
• Separate the elements of a row with blanks or commas.
• Use a semicolon, ; , to indicate the end of each row.
• Surround the entire list of elements with square brackets, [ ] .
You can enter matrices into MATLAB in several different ways:
• Enter an explicit list of elements.
• Load matrices from external data files.
• Generate matrices using built-in functions.
• Create matrices with your own functions in M-files.
To enter matrix, simply type in the Command Window
The element in row i and column j of A is denoted by A(i , j)
A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]MATLAB displays the matrix you just entered.
A =16 3 2 135 10 11 89 6 7 124 15 14 1
For example, A(4,2) is the number in the fourth row and second column.
>> A(4,2)ans =
15
>> [A B]
>> size(ans)
>> [A ; B]
SubmatrixSubmatrix
JuxtapositionJuxtaposition
>> A(1,:)
>> A(:,2)
>> A(3:4,1:2)
>> B = [9 8 2 5 ; 4 5 6 7 ; 2 1 3 4]
The Colon OperatorThe Colon Operator
>> 1:10The colon, :, is one of the most important MATLAB operators.
To obtain nonunit spacing, specify an increment.
For example,
>> 100:-7:50and
>> 0:pi/4:pi
linspace function creates row vectors with equally spaced elements.
>> u = linspace(0.0,0.25,5)>> v = linspace(0,9,4)’>> x = linspace(0,pi/6,6*pi);
>> s = sin(x);>> c = cos(x);
>> t = tan(x);
>> [x’ s’ c’ t’]
LinspaceLinspace
Workspace BrowserWorkspace Browser
The MATLAB workspace consists of the set of variables (named arrays) built up during a MATLAB session and stored in memory.
You add variables to the workspace by using functions, running M-files, and loading saved workspaces.
To view the workspace and information about each variable,
use the Workspace browser, or use the functions who and whos.
Example 2.1 Transportation route analysisExample 2.1 Transportation route analysis
The following table gives data for the distance travel along five truck routes and thecorresponding time required to traveled each route. Use the data to compute the average speed required to drive each route. Find the route that has the highest average speed.
